When I cut and paste part of an image to a new file I am getting a back ground layer that is slightly larger than the size of the image.
How do I prevent Photoshop adding a background layer or at least make it the same size as the image dimension.
To my knowledge, there's always a background layer in Photoshop, but you can remove it by double-clicking it and dragging it in the little trash on the bottom of the layers panel.
Regarding the slightly larger background, It could be caused by your selection having a "feather" on it.
When you select something with a feather value, you new Photoshop file where you will paste the image you copied will be slightly bigger because of this.
Try setting the feather to 0 and see if it still does this.